Joshua Drewitt

Applications of real-analytic modular forms

The space of real-analytic modular forms was recently introduced by Francis Brown. One reason this space is of great interest is because it contains or intersects various classes of important modular objects, such as classical modular forms, weakly anti-holomorphic forms and Maass wave forms. Therefore, the space of real-analytic modular forms can be viewed as a unifying tool for all these individual subspaces. The purpose of this talk is to introduce you to this space and to demonstrate a few of its interesting proper- ties and applications. We give examples of real-analytic modular forms, discuss the period polynomials and L-functions related to this space, and see how these forms connect to the study of string theory in physics.